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The second project of the semester was the predator prey model. Lee, Nick, and I worked on this project. Choose a system of equations, with values of parameters and initial conditions to investigate. Plot both solution curves as a function of time and as phase space plots.
Begin with the following equation. To solve we first need to use separation of variables. You end up with the following. Next you multiply both sides by e. We end with the following. If the temperature of .
Our last objective was to find exact solutions to the systems of differential equations we made in the last assignment. The first step was to put the two equations in matrix form with the eigenvalues -3,1,1,-3 in one matrix and y1 and y2 in the other matrix. We had to find a value for x so that the matrix equation.
For this project we were given two first order linear differential equations. Our goal is to use the characteristic equation. To find values for the constants. In each case the eigenvalues. Are the roots for the characteristic equation. In the code, we replaced the constants.